Ocean Heat, From the Tropics to the Poles

The heat being captured by the increasing load of carbon dioxide and other greenhouse gases in the atmosphere is subsequently transferred into the oceans for storage. This process — global warming — has raised the temperature of the biosphere by 1°C (or more) since the late 19th century.

Heat introduced into any material body at a particular point will diffuse throughout its volume, seeking to smooth out the temperature gradient at the heating site. If heat loss from that body is slow or insignificant, then a new thermal equilibrium is eventually achieved at a higher average temperature.

Thermal equilibrium does not necessarily mean temperature homogeneity, because the body may have several points of contact with external environments at different temperatures that are held constant, or with other external thermal conditions that must be accommodated to. Equilibrium simply means stable over time.

The heat conveyed to the oceans by global warming is absorbed primarily in the Tropical and Subtropical latitudes, 57% of the Earth’s surface. The Sun’s rays are more nearly perpendicular to the Earth’s surface in those latitudes so they receive the highest fluxes of solar energy, and oceans cover a very large portion of them.

That tropical heat diffuses through the oceans and is also carried by ocean currents to spread warmth further north and south both in the Temperate zones (34% of the Earth’s surface) and the Polar Zones (8% of the Earth’s surface).

What follows is a description of a very idealized “toy model” of heat distribution in the oceans, to help visualize some of the basics of that complex physical phenomenon.

Heat Conduction in a Static Ocean

The model is of a stationary spherical globe entirely covered by a static ocean of uniform depth. The seafloor of that ocean is at a constant temperature of 4°C (39°F), the surface waters at the equator are at 30°C (86°F), and the surface waters at the poles are at -2°C (28°F). These temperature conditions are similar to those of Earth’s oceans. These temperature boundary conditions are held fixed, so an equilibrium temperature distribution is established throughout the volume in the model world-ocean. There is no variation across longitude in this model, only across latitude (pole-to-pole). (See the Notes on the Technical Details)

Figure 1 shows contours of constant temperature (isotherms) throughout the depth of the model ocean, from pole to pole. The temperature distribution is shown as a 3D surface plotted against depth, which is in a radial direction in a spherical geometry, and polar angle (from North Pole to South Pole).

Figure 2 is a different view of the temperature distribution. Three regions are noted: The Tropical Zone (from 0° to 23° of latitude, north or south) combined with the Subtropical Zone (from 23° to 35° of latitude, north or south); the Temperate Zone (from 35° to 66° of latitude, north or south); and the Polar Zone (from 66° to 90° of latitude, north or south).

The model temperature distribution is perfectly stratified — isotherms uniform with depth — in the Tropical-Subtropical Zones, from 30°C at the surface at the equator, to 4°C at the seafloor. On entering the Temperate Zones, the isotherms arc up into a nearly radial (vertical) orientation. In the small portions of the planetary surface covered by the Polar Zones the isotherms are now more horizontally stratified because the surface waters are chillier that the those at the seafloor.

Figure 3 shows the streamlines of heat flow (the temperature gradient) for this temperature distribution. At the equator the heat is conducted down from the 30°C surface to the 4°C seafloor. As one moves further away from the equator the streamlines become increasingly lateral, until they are entirely so at 35° of latitude (north or south) where the model surface waters are at 19°C. The heat flow is entirely horizontal at this latitude, which separates the Subtropical and Temperate Zones; tropical heat is being conducted laterally toward the poles. In the Polar Zones the heat flow is up from the lower depths because the surface waters are chiller than those at depth, and because there is too little temperature variation with distance along the surface to drive a lateral heat flow.

Thermally Driven Surface Currents

Much oceanic heat is distributed by currents, and many of these occur along the surface.

The average speed of the Gulf Stream is 6.4km/hr (4mph), being maximally 9kph (5.6mph) at the surface but slowing to 1.6kph (1mph) in the North Atlantic, where it widens (information from the National Oceanic and Atmospheric Administration, NOAA).

Heat-driven equator-to-poles surface currents on the model ocean were estimated from the combination of the pole-to-pole surface temperature distribution, and thermodynamic data on liquid water. (See the Notes on the Technical Details)

The pressure built up by tropical heat in the model ocean’s equatorial waters pushes surface flows northward (in the Northern Hemisphere) and southward (in the Southern Hemisphere): from a standstill at the 30°C equator; with increasing speed as they recede from the equator, being 2kph (1.3mph) where the surface waters are at 25°C (77°F); a continuing acceleration up to a speed of 2.8kph (1.7mph) at the 35° latitude (the boundary between the Subtropical and the Temperate Zones); and an ultimate speed of 3.6kph (2.2mph) at the poles.

The currents are converging geometrically as they approach the poles, so a speed-up is reasonable. Logically, these surface currents are legs of current loops that chill as they recede from the equator, plunge at the poles, run along the cold seafloor toward the equator, and then warm as they rise to the surface to repeat their cycles.

An equator-to-pole average speed for these model surface currents is 2.8kph (1.7mph). Their estimated travel times along the 10,008km surface arc (for a model world radius of 6,371km, like that of a sphericalized Earth) is 3,574 hours, which is equivalent to 149 days (0.41 year).

Greater Realities

The model world just described is very simple in comparison to our lovely Earth. Since it does not rotate, it does not skew the north-south flow of currents that — with the help of day-night, seasonal, and continental thermodynamic inhomogeneities — creates all of the cross-longitudinal air and ocean currents of our Earth.

The irregularity of seafloor depth on Earth also redirects cross-latitudinal (pole-to-pole) and cross-longitudinal bottom currents, as do the coastlines of the continents; and the very slight and subtle changes in seawater density with temperature and salinity — neither of which is distributed uniformly throughout the body of Earth’s oceans — also affect both the oceans’s volumetric temperature distributions, and the course of ocean currents.

Recall that the model ocean is bounded by constant imposed temperature conditions at its seafloor (4°C) and surface waters (a particular temperature distribution from 30°C at the equator, to -2°C at the poles). Since this model world is otherwise suspended in a void, if these boundary conditions were removed the oceanic heat concentrated at the equator would diffuse further into the watery volume, seeking to raise the temperatures of the poles and seafloor while simultaneously cooling the equatorial region. The ultimate equilibrium state would be an ocean with a constant temperature throughout its volume.

Additionally, if it is also assumed that the now “liberated” model ocean-world can radiate its body heat away — as infrared radiation into the void of space — then the entire planet with its oceanic outer shell slowly cools uniformly toward -273.16°C (-459.69°F), which is the “no heat at all” endpoint of objects in our physical Universe.

When our Earth was in its Post-Ice Age dynamic thermal equilibrium, the “heat gun” of maximal insolation to the Tropics and Subtropics warmed the oceans there; a portion of that heat was conducted and convected into the Temperate Zones and toward the Poles; where the “ice bags” of masses of ice absorbed seasonal oceanic heat by partially melting — which occurs at a constant temperature — and then refreezing. Also, the atmosphere did not trap the excess heat radiated into space. In this way cycles of warming and cooling in all of Earth’s environments were maintained in a dynamic balance that lasted for millennia.

What has been built up in the atmosphere since about 1750 is an increasing load of carbon dioxide gas and other greenhouse gases, which have the effect of throwing an increasingly heated “thermal blanket” over our planet. Now, both the heat conduction pathways and the heat convection currents, described with the use of the model, convey increasing amounts of heat energy over the course of time. As a result the masses of ice at the poles are steadily being eroded by melting despite their continuing of cycles of partial re-freezing during winter, and additional melting during summer.

Simple mathematical models can help focus the mind on the fundamental processes driving complex multi-entangled physical realities. From there, one can begin assembling more detailed well-organized quantitative descriptions of those realities, and then using those higher-order models to inform decisions regarding actions to be taken in response to those realities, if responses are necessary. This point of departure from physics plunges you into the world of psychology, sociology, economics, politics, and too often sheer madness. I leave it to another occasion to comment outside my field of expertise about all that.

Notes on the Technical Details

The cylindrically symmetric equilibrium temperature distribution for a static ocean of uniform depth, which entirely covers a spherical planet, was solved from Laplace’s equation. The temperature of the seafloor everywhere is 4°C, the surface waters at the Equator are at 30°C, and the surface waters at the poles are at -2°C. The variation of surface water temperature with respect to polar angle (latitude) is in a cosine squared distribution. Displays of the 3D surface T(r,ɵ) show isotherms down through the ocean depths at all polar angles (ɵ). The contour lines on the stream function associated with T(r,ɵ) are heat flow streamlines, the paths of the heat gradient (which are always perpendicular to the isotherms).

Bernoulli’s Theorem was applied to surface flow from the equator to the poles (no radial, nor cross-longitudinal motion) for incompressible liquid water with thermal pressure given by:


for R equal to the planetary radius to the ocean surface; Tp=-2°C; and using thermodynamic data for water between 32°F (0°C) and 100°F (37.8°C) that indicates a thermal pressure equal to 62.25kg/m-sec^2 in liquid water at 0°C; and that the density of water is essentially constant at 1000kg/m^3 (for the purposes of this model) within the temperature range of the data surveyed.

Inserting P(T°C) into the Bernoulli Theorem definition of equator-to-pole lateral (cross-latitudinal) velocity gives a formula for that velocity as a function of polar angle:



for Te=30°C, and ± for northward (in the Northern Hemisphere) or southward (in the Southern Hemisphere) surface flows.



A Formula For U.S. Election Outcomes


A Formula For U.S. Election Outcomes

I am wondering what the chances are for significant U.S. government action on the following ten issues, before 2022:

1. Equity of taxation
(popular/leveling vs. corporate/plutocratic),
2. Extract money from politics, kill Citizens United
(prosecute influence peddling and financial crimes),
3. climate change action (Green New Deal),
4. cut war spending, end the Yemen War
(and cut military-corporate subsidies),
5. Medicare-for-All
(versus insurance company gouging),
6. Social Security expansion
(versus general impoverishment for fat cat gains),
7. fund and staff welfare programs
(food, shelter, childcare, post-disaster assistance),
8. immigration reform and smart liberalization,
9. public school upgrades and teacher funding
(versus vouchers for resegregation; free college),
10. end subsidies for Christian xenophobia bigotry
(pursue Civil rights prosecutions, and Reparations).

This depends on what kinds of administrations we get as a result of national and state elections in 2020 and 2022. So, I devised a mathematical model of U.S. voting outcomes based on voter political affiliations and voting preferences. My aim is to have a tool to quantify my guesses about future election outcomes, so as to improve my speculations on when and to what degree desirable action will be taken on the ten issues stated. This exercise was better than being glum, dejected and confused about American politics, and this essay summarizes my findings. I based my model on voting behavior during U.S. presidential (quadrennial) elections instead of on midterm elections, but why not use it for both?

There were 7 of steps in devising this model: 1, determining the fractional composition of the American electorate by age brackets (15 of them); 2, finding the percent voter turnout by age bracket; 3, finding the party identification (both formal affiliation and casual identification) proportionally by age bracket; 4, collapsing all that data into the percent of the voting population that favors each of the three major U.S. political ideologies (from least to most amorphous): Republican, Democratic, and Independent; 5, examining the tabulated numerical date to divine the most general and instructive relationship, dependent on the fewest number of parameters, to devise a specific correlating and predictive mathematical formula; 6, calculate hypothetical results from this formula and then compare them (to the extent possible) with data on prior election outcomes; and 7, generalize the initial formula into an easily used estimating tool.

The Data

My source for population data was the U.S. Census Bureau [1]. On July 1, 2017, the US population was (officially) 325,719,178, and the voting age (18-85+) population (without considering legal barriers) was 252,018,630. I used data published by Charles Franklin on voter turnout as a function of age (https://medium.com/@PollsAndVotes/age-and-voter-turnout-52962b0884ef), [2]. I collapsed Franklin’s smooth data curve (for voter turnout, by age, to presidential elections) into 15 single values of percent turnout, one for each of the 15 age brackets: 18-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75-80, 80-84, 85 and up. Turnout for teen and early 20s voters is 47%-55% (17%-25% for midterms), and turnout increases steadily with age, reaching a broad peak between 80% and 85% for voters 55 to 80 years old (70% to 73% for ages 62 to 79, for midterms). The population between 18 and 34 years (16 year span) is 75,913,971; the population between 60 and 79 years (19 year span) is 58,412,409. The population between 55 and 79 (24 year span) is 80,420,365; the population between 18 and 39 (21 year span) is 97,145,968. Voters between the ages of 18 and 29 (11 year span) contribute 17% of the presidential vote; voters between the ages of 50 and 59 (9 year span) contribute 19% of the presidential vote. Ah, poor youth, condemned to struggle and strive in a country (and world) shaped and directed by the crabbed and brittle prejudices of a smaller number of futureless self-satisfied property owners.

Party affiliation is of two types: being a reliable voter to a party you are registered with, or being an independent voter who will admit to “leaning” (in the voting booth) to the Democrats or Republicans, especially when you are alarmed or enthused about a particular election or issue. Those voters who refuse to declare a duopolistic party allegiance or even a “lean” are the staunch Independents. The Gallup organization has published data on the percent of voters who are Democrats, Republicans, and Independents, as well as leaners to the Democrats and Republicans, by age (https://news.gallup.com/poll/172439/party-identification-varies-widely-across-age-spectrum.aspx), [3]. Using this data, I lumped leaners in with declared party loyalists (respectively, for Republicans and Democrats), and then for each of the 15 age brackets assigned three numerical factors for the percentage of the age bracket voting in each of three modes: Republican, Democratic or Independent. From all the data described to this point, I was able to calculate, for each age bracket, the percent of the presidential vote that went to the Republican and Democratic parties, and to the Independent category. I summed up the results for the 15 age brackets to get an overall composition of the entire voting population, and rounded the final numbers slightly for convenience, to arrive at: 45% Democratic, 40.5% Republican, and 14.5% Independent. I will call this the “baseline.”

Note that all the data described above refers to conditions between 2014 and 2017.

The Formula (!)

If people voted consistently with their declared affiliations, we would have a continuous sequence of Democratic Party administrations; but people don’t, so we have flux and upheaval. In fact, the outcome of our national elections is driven by the surreptitious faithlessness of our tight-lipped (to pollsters at least) Independent voters. Our staunch Independent voters number between 1-in-8 (12.5%) to 1-in-5 (20%) of the voting population, and this fraction varies geographically and over time, in mysterious ways. What actually happens with Independents in the privacy of their voting booths is that they make individual choices about individual issues and candidates, and for each of these they vote in one of three ways: Democratic, Republican, or for one of the myriad of Independent options available, including abstention. So, the 14.5% (to take a fixed number for now) of the voting population that is incorrigibly Independent actually splits into three fractions during voting (quantified here as percentages of the Independent voting population only): I%D, I%R, and I%I. The label I%D represents the percentage of the Independents who voted Democratic in a particular election. Similarly, I%R corresponds to the percentage of the Independents who supplied Republican votes, and I%I corresponds to the percentage of the Independents who remained purely Independent. Note that I%D + I%R + I%I = 100%.

The 4.5% advantage Democrats have over Republicans nationally, based on my calculations (the baseline), can easily be overcome by a 5% or greater net contribution of Republican votes from the Independents. For example, if the Independent population splits: 50% Republican, 5.2% Democratic, and 44.8% staunch Independent (50% + 5.2% + 44.8% = 100% of the Independent population) then they contribute, nationally: 7.2% for Republicans (50% of the 0.145 fraction of the national vote made up of Independents), 0.8% for Democrats (5.2% of their 0.145 national fraction), and 6.5% (44.8% of their 0.145 national fraction) for Independent candidates. The result for the national election becomes: 47.7% Republican (40.5% + 7.2%), 45.8% Democratic (45% + 0.8%), and 6.5% Independent (14.5% – 7.2% – 0.8%). Note that 47.7% + 45.8% + 6.5% = 100% of the national vote. In this case the Republicans win the election with a 2.0% lead (with slight rounding).

By calculating several examples, as just shown, one can arrive at the following equation for election outcomes (for the duopoly horse race).

D-R = 4.5% + [0.145 x (I%D – I%R)].

In words: the percentage difference between Democrats and Republicans in national elections is equal to 4.5% plus the fraction 0.145 multiplied by the difference between the percentage of the Independent voting population that voted Democratic, and the percentage of the Independent voting population that voted Republican. The calculation for the previous example is as follows:

D-R = 4.5% + [0.145 x (5.2% – 50%)] =
D-R = 4.5% + [0.145 x (-44.8%)] =
D-R = 4.5% + [-6.5%]
D-R = -2%

Democrats lose, numerically, by 2%. Also, the actual vote going to Independents nationally is:

Actual Independent Vote Nationally =
14.5% (Independents) – 7.2% (to R) – 0.8% (to D) = 6.5%.

After playing a while with the duopoly horse race estimator formula, give above, I realized one can generalize it further.

D-R = D0 + [Fl x (I%D – I%R)].

D-R = percentage difference between Democrats and Republicans, from election.
D0 = percentage advantage (+) or disadvantage (-) for Democrats, based on affiliations.
FI = the fraction (not percentage) of the voting population that is Independent.
I%D = the percentage of the Independent population that chooses D (this time).
I%R = the percentage of the Independent population that chooses R (this time).
I%I = the percentage of the Independent population that remains I (this time).
Note that: I%D + I%R + I%I = 100%.

So far here, I have used D0 = 4.5%, and FI = 0.145. However, you can choose different numbers based on your own survey of population, voter turnout and party affiliation data, or on your intuition about a particular electoral contest. As mentioned earlier, estimates of FI can range between 0.125 (1/8) to 0.2 (1/5), and perhaps beyond.

Comparing To Previous Elections

I have not found data on the population sizes and voting splits of the Independent voting contingent in previous elections. It would be nice to validate the formula using such data. While the assumptions underpinning this model may not be representative of conditions in all prior US elections, we can nevertheless use prior election results to calculate inferences about what might have been the voting behavior of Independent voters in the past. To do that, we assume that the baseline (40.5% R, 14.5% I, 45% D), which was calculated from 2014-2017 data, has been constant (or nearly constant) since 1968. Here are the calculated inferences on how Independents voted in elections since 1968, based on the known national outcomes.

1968, Nixon
R. Nixon (R) 43.4% vs. H. Humphrey (D) 42.7% vs. G. Wallace (I) 13.5%
Remainder of the national vote is 0.4%
Independents contribute 14.5% of the national vote
Independents split: 77.2% (Wallace), 20% (R), 0% (D), 2.8% (I).

1972, Nixon
R. Nixon (R) 60.7% vs. G. McGovern (D) 37.5%
Remainder of the national vote is 1.8%
Independents contribute 14.5% of the national vote
Independents split: 87.6% (R), 0% (D), 12.4% (I)

1976, Carter
J. Carter (D) 50.1% vs. G. Ford (R) 48%
Remainder of the national vote is 1.9%
Independents contribute 14.5% of the national vote
Independents split: 51.7% (R), 35.2% (D), 13.1% (I)

1980, Reagan
R. Reagan (R) 50.7% vs. J. Carter (D) 41% vs. J. Anderson (I) 6.6%
Remainder of the national vote is 1.7%
Independents contribute 14.5% of the national vote
Independents split: 42.8% (R), 0% (D), 45.5% (Anderson), 11.7% (I)

1984, Reagan
R. Reagan (R) 58.8% vs. W. Mondale (D) 40.6%
Remainder of the national vote is 0.6%
Independents contribute 14.5% of the national vote
Independents split: 95.9% (R), 0% (D), 4.1% (I)

1988, Bush Sr.
G.H.W. Bush (R) 53.4% vs. M. Dukakis (D) 45.6%
Remainder of the national vote is 1.0%
Independents contribute 14.5% of the national vote
Independents split: 89% (R), 4.1% (D), 6.9% (I)

1992, Clinton
W. Clinton (D) 43% vs. G.H.W. Bush (R) 37.4% vs. R. Perot (I) 18.9%
Remainder of the national vote is 0.7%
Independents contribute 14.5% of the national vote
Independents split: 0% (R), 0% (D), 95.2% (Perot), 4.8% (I)

1996, Clinton
W. Clinton (D) 49.2% vs. R. Dole (R) 40.7% vs. R. Perot (I) 8.4%
Remainder of the national vote is 1.7%
Independents contribute 14.5% of the national vote
Independents split: 1.4% (R), 29% (D), 58% (Perot), 11.6% (I)

2000, Bush Jr.
G. Bush (R) 47.9% vs. A. Gore (D) 48.4%
Remainder of the national vote is 3.7%
Independents contribute 14.5% of the national vote
Independents split: 51% (R), 23.5% (D), 25.5% (I)
Bush appointed despite a 0.5% deficit.

2004, Bush Jr.
G. Bush (R) 50.7% vs. J. Kerry (D) 48.3%
Remainder of the national vote is 1.0%
Independents contribute 14.5% of the national vote
Independents split: 70.3% (R), 22.8% (D), 6.9% (I)

2008, Obama
B. Obama (D) 52.9% vs. J. McCain (R) 45.7%
Remainder of the national vote is 1.4%
Independents contribute 14.5% of the national vote
Independents split: 35.9% (R), 54.4% (D), 9.7% (I)

2012, Obama
B. Obama (D) 51.1% vs. M. Romney (R) 47.2%
Remainder of the national vote is 1.7%
Independents contribute 14.5% of the national vote
Independents split: 46.2% (R), 42.1% (D), 11.7% (I)

2016, Trump
D. Trump (R) 46.1% vs. H. Clinton (D) 48.2%
Remainder of the national vote is 5.7%
Independents contribute 14.5% of the national vote
Independents split: 38.6% (R), 22.1% (D), 39.3% (I)
Trump appointed despite a 2.1% deficit.

The 2.1% Republican Credit

In the 2000 election, G. Bush (R) had a 0.5% deficit and was still appointed the 43rd President of the United States of America.

In the 2016 election, H. Clinton (D) gained a 2.1% lead over D. Trump (R) – the same lead J. Carter (D) used to win in 1976 – and yet Trump was appointed the 45th President of the United States of America.

These “deficit wins” were due to a combination of nefarious factors: the Electoral College, pro-Republican judicial bias, voter suppression efforts (in both R and D varieties), vote counting sabotage, and undoubtedly other forms of creative incompetence.

So, today we must assume that because of embedded structural irregularities in the American electoral mechanism, that Democrats must gain more than a 2.1% advantage over Republicans in order to win national elections.

I easily concede that my simple clean mathematical formula does not contain the full range of rascally dirty realities in American electoral spectacles.

Dreams Of DSA Utopia

Could a significant politically leftward sentiment ever take hold among the Independent voting population, and this cause a leftward shift in electoral outcomes? The more socialist (or democratic-socialist, or progressive, of left) the legislators, executives and administrations that result from near-future elections, the more likely the ten issues I listed at the beginning would get serious attention – and action!

W. Clinton (D) won in 1996 with an 8.5% advantage. His Democratic administration was pure corporate, no different from center-right Republican policy before Reagan. I assume that if the voting population turned further away from Republicans, and more in favor of the most socialist-oriented Democratic candidates, that the resulting Democratic administrations would be less corporate-oriented (yes, I know this is magical thinking at present).

So, perhaps a Democratic victory with a 12.5% advantage would result in a Democratic administration that is a half-and-half mixture of corporate (DNC type) Democrats and socialist (DSA type) Democrats, and then some serious nibbling would occur on the ten issues. Mathematically, this could result if the hypothetical Independents split: 55.2% (D), 0% (R), and 44.8% stayed pure (I). The projected national election result would be 53% Democratic, 40.5% Republican, and 6.5% Independent.

An even better though less likely occurrence would be a socialist Democratic Party that gains a 16.5% electoral advantage, driving the Republican Party to extinction (instead of us!). Using the formula, we can infer an Independent split of: 82.8% (D), 0% (R), 17.2% pure (I). The projected national election result would be 57% Democratic, 40.5% Republican, 2.5% Independent.

The ultimate fantasy is of all Independents becoming enthusiastic DSA socialists, so they would add their 14.5% of the national vote to a socialist Democratic Party, with a projected electoral result of: 59.5% Democratic (pure DSA), 40.5% Republican, 0% Independent. An electorate that could accomplish this would empower national and state administrations that would address the ten issues listed earlier, with vigor and all the resources – human, material, and intangible – available to this rich nation.

However improbable the last scenario – of a Socialist political tsunami – appears in the United States of today, I think it is better to keep it in mind as a vision (more easily done if you are young), rather than acidly disparaging and brusquely dismissing it (more likely done by the old and bitter), because it can help motivate useful activism and kind action from those who want a better world with fairer politics and economics, and know that it is humanly possible to get it.


[1] Annual Estimates of the Resident Population for Selected Age Groups by Sex for the United States, States, Counties, and Puerto Rico Commonwealth and Municipios: April 1, [use above title to search in “2017 Population Estimates,” link below is just a start]

[2] Age and Voter Turnout (Charles Franklin)

[3] Party Identification Varies Widely Across the Age Spectrum